h
4120
Table IV : Estimated Molecular Structure Parameters Used to Calculate the Free-Energy Functions of the Hydroxides Fe
(M-01, A re (O-H), A 0-H (2), stretch, cm-1 M-OH, stretch, cm-1 re
0-M-O, bend, cm-1 M-0-H (2), bend, cm-1 MO-H (2), torsion, cm-1 M-0-H angle, deg Electronic fef ( 1600'K), eu Fef (1600'K), eu
1.8
1.8
0.96 3650 605 770 210 1170 230 105' -5.75
0.96 3650 365 460 125 1170 230 105' -5.54
-82.56
Table V: Average Bond Energies, O'K, of Fe, Co, and Ni Difluorides, Dihydroxides, and Dichlorides"
Ni
co
-83.50
1.8 0.96 3650 650 820 222 1170 230 105' -4.89 -81.50
sensitivity of the results to a number of manipulations of the structural parameters, e.g., assuming a trans configuration or free internal rotations of the OH groups, it is the authors' opinion that the values should be correct to about *2 kcal, at least in comparison to the halides.
T
M-F, kcal M-OH, kcal M-Cl, kcal
Fe
co
114.3 98.2 94.9
110.8 91.9 85.3
Xi
109.3 91.2 86.0
Data for dichlorides and difluorides derived from Allen17 and Brewer, et aL2*
Thus it appears that treating the gaseous hydroxides as pseudohalides is a useful concept, and consistently with this, the bond energies may be taken to be approximately midway between the fluorides and chlorides.
Acknowledgment. This study, a contribution from the Laboratory for Research on the Structure of Matter, University of Pennsylvania, was supported by the Advanced Research Projects Agency, Office of the Secretary of Defense.
NOTES
The Influence of Pressure on the Velocity Constants of Bimolecular Ionic Reactions in Aqueous Solution
by E. A. Moelwyn-Hughes Department of Physical Chemistry, The University, Cambridge, England Accepted and Transmitted by The Faraday Society
(March 10, 1967)
Concerning E,,, the nonelectrostatic component of the activation energy, little is known. The electrostatic component, x.4zBE2/Dr,is given by the electrovalencies, x , the electronic charge, E , the dielectric constant, D , and the distance apart of the centers of the charges in the activated complex. By treating Zo,E,, and r as temperature independent, eq 1 has been shown adequate to explain high and low values of the preexponential term in the Arrhenius equation, In kz0 = In Azo - E A / R T . We have2
A'O = The bimolecular velocity constant for ionic reactions at zero ionic strength can be represented by the equation' In
k20
- ERT, - DrkT
= In ZZ0 -
ZAZBE'
(1 1
where Zois the standard binary collision frequency in a solvent of dielectric constant D at temperature T. The Journal of Physical Chemistry
Z~O~-ZA"B~*L/~DI.
(2)
where L = -(a In D / b T ) p . The object of this communication is to find to what extent eq 1 may account for the variation of with respect to pressure a t constant temperature. ~~
~
(1) J. A. Christiansen, 2.Physik. Chem., 113, 35 (1924); G . Scatchard, Chem. Rev., 10, 229 (1932). (2) E. A. Moelwyn-Hughes, Proc. Roy. SOC. (London). A155. 308 (1936).
~
~
NOTES
4121
By differentiating eq 1 and making use of the equation (3) we obtain for the molar volume of critical activation the expression
+
Av, = -RT(?)~ b In Zzo
(z)
critical interionic separation afforded by eq 7 compare favorably with the values found by numerous independent method^.^ It therefore appears that the effect of pressure on the velocity of ionic reactions in aqueous solution is significantly, if not predominantly, to be traced to the effect of pressure on the dielectric constant of the medium.
Table I: Critical Interionic Distances Afforded by Eq 7
b In D Reaction
where NOis Avogadro’s number. A rough estimate of the first term on the right-hand side may be made by assuming 22 to be proportional, directly or inversely, to the viscosity of the solvent. For water a t 30°, the contribution to AVc is -1.15 or +1.15 cc, respectively. Nothing is known about (bE,/bP)T except that it may be considerable. If the reacting ions and the complex formed from them are all spherical, with evenly distributed charges, it is possible in principle to evaluate the term (b In r / b P ) , in terms of the partial ionic compressibilities, pi, as Hamann3 has shown in the case of the ionization of ammonium hydroxide. None of the reacting species to be considered approaches such a simple electrostatic model and we remain in ignorance of the magnitude of ( b In ~ l b P ) ~ To. evaluate the remaining term in eq 4, it is convenient to use the compressibility, p, and the density, p , of the solvent, as b In D
b In D
(dp), = (
F
)
L
E
)
T
0
Temp,
Dr
+ OH+ NCOCHzBrCOO- + S a O a l Co(NHs)dBr*++ OHCHaClCOO“I+
Ref
“C
Avc
ZAZB
u b
40 60 24.5 30
-6.1 +14 -4.8 f8.5
+l
c c
-1 +2 -2
r, A
1.75 0.76 4.46 2.52
R. 0. Gibson, E. W. Fawcett, M. W. Perrin, and E. G. Williams, Proc. Roy. SOC.(London), A150, 223 (1935); 154, 684 (1936). * H. G. David and S. D . Hamann, Tram. Faraday Soc., 50,1188 (1954). C. T. Buriss and K . J. Laidler, ibid., 51, 1497 (1955).
Christiansen’s theory of bimolecular reactions in solution has been applied to interpret the effect of pressure on the velocity constants of ionic reactions a t zero ionic strength. It is concluded that the effect of pressure on the reaction rate is significantly, if not predominantly, to be traced to the effect of pressure on the dielectric constant of the medium. (3) “Physicochemical Effects of Pressure,” Butterworth and Co., Ltd., London, 1957. (4) I. S. Jacobs and A. W. Lawson, J . Chem. Phys., 2 0 , 1161 (1952). (5) E. A. Moelwyn-Hughes, “Kinetics of Reactions in Solution,” 2nd ed, Oxford University Press, London, 1947, p 106.
=
The contribution to AVO ascribable to the effect of pressure on the dielectric constant is thus The Dehydrogenation Reaction of Methanol
NGAxBE~P b In D
AVc =
-
Dr
(
z
)
T
(6)
The compressibility of water at 20” is 4.68 X 10“ atm-I and ( b In D / b In p ) T is 1.34 0.02.4 Hence, with AVc in cubic centimeters per mole and r in angstrom units
*
(7) Because AVc varies with the pressure, we have used the experimental values relating to low pressures. These are given in Table I, where, unfortunately, only two of the data refer to temperatures near to that for which eq 7 applies. For these two reactions, the values of the
during Electrosorption on Platinum
by R. E. Smith, H. B. Urbach, and ?;. L. Hatfield U.S. Navy Marine Engineering Laboratory, Annapolis, Maryland (Received March 88, 1967)
Radiometric evidence of a reduction of hydrogencarbon bond strengths in the methanol molecule when adsorbed from solution on a platinum black electrode has been obtained in a continuing study1 of electrosorp(1) R. E. Smith, H. B. Urbach, J. H. Harrison, and N. L. Hatfield, J . Phya. Chem., 71, 1250 (1967).
Volume 71. Number 1.9 November 1967
